The figure shows an arrangement of an equi-convex lens and a concave mirror. A point object O is placed on the principal axis at a distance `40 cm` from the lens such that the final image is also formed at the position of the object. If the radius of curvature of the concave mirror is `80 cm,` find the distance d. Also draw the ray diagram. The focal length of the lens in air is `20 cm.`

Answer

C

Explanation

`1/20=(1.5-1)(1/R-1/(-R))`
`:. R=20 cm`
Appying `(mu_2)/v-(mu_1)/u=(mu_2-mu_1)/R,` twice with the
condition that rays must fall normally on the
concave mirror.
`1.5/(v_1)-1.2/(-40)=(1.5-1.2)/(+20)…..(i)`
`2.0/(d-80)-1.5/(v_1)=(2.0-1.5)/(-20)....(ii)`
Solving Eqs. (i) and (ii), we get
`d=30 cm`
and `v_1=-100 cm`
The ray diagram is as shown in figure.